Surface temperature gradients and rates of internal heat evolution at criticality for generalized heat transfer (arbitrary Biot number)
Abstract
The dependence on the heat-transfer conditions (Biot number, Bi) of the temperature gradient at the surface, Γ, of an exothermic reactant mass at criticality is presented. Bodies of slab, cylindrical and spherical geometry have the same values of Γcr at the Frank-Kameneskii extreme (Bi→∞, Γcr= 2) and also at the Semenov extreme (Bi= 0, Γcr= 0). For general boundary conditions the critical surface temperature gradient depends on the Biot number and shape.